In the field of Acoustics, there exist only four commonly-accepted means of changing acoustic phenomenon: absorption, reflection, refraction, and diffusion. Absorption is the process in which acoustic energy comes in contact with a material that converts the energy into heat. Reflection is the process in which acoustic energy strikes a material and is redirected largely unchanged. The angle of incidence of the sound source relative to the reflector is equal to the angle of reflection. In this way, sound behaves very much like a rubber ball striking a hard flat surface. Refraction is the process in which acoustic energy bends around or is blocked by objects.
Diffusion is the process in which acoustic energy comes in contact with a rigid, non-uniform shape with lots of surface area and scatters in many different directions. Diffusion causes a measurable reduction in acoustic energy because the energy is spread over a large surface area. When a sound heads toward a surface that is uneven, non-uniform and with a varied texture the sound does not strike the surfaces all at the same time. The resulting reflections return with small changes in timing or phase. A good diffuser causes both scattering, creating reflections in many directions, and changes in phase, creating reflections at many times. One measure of diffusion involves examining how an impulse of acoustic energy is smeared or spread out over an amount of time.
The classic historical concert halls all possessed many irregular surfaces. Alcoves with sculptures and heavily encrusted and ornamented moldings act as excellent if unintentional diffusers. The problem in modern acoustics is to find better diffusive shapes that are easier to manufacture than hand carved moldings and marble sculpture.
Diffusers are considered to be either one dimensional or two dimensional. Sound striking a single-dimensional or 1D diffuser would be diffused in a semi-circular pattern away from the diffuser in a single horizontal dimension. A two-dimensional or 2D diffuser would diffuse sound in a hemispherical pattern, both horizontally and vertically.
Manfred R. Schroeder is the father of modern acoustic diffusion research. Nearly all diffusers designed and manufactured today are at least partially based on his ground breaking research. He was the first scholar to explore the use of rectilinear wells of different depths as a means of diffusing acoustic energy. Schroeder applied the idea of the light and x-ray scattering property of crystals to the scattering of acoustic energy. The concept of this type of diffusion is called reflection phase grating
Schroeder explored the use of both quadratic residue and primitive root number sequences to define the depth of a series of wells in acoustic diffusers. These number sequences have been employed time and again by different diffuser designers. For whatever reason, Manfred Schroeder did not explore either quadratic residue diffusers or primitive root diffusers in a commercial sense. This was largely done by Peter D'Antonio of RPG Diffuser Systems, Inc.
Schroeder's one-dimensional diffusers consist of a series of rectilinear wells each with the same height and width, but with varying depths. The depths of the wells determine the lowest frequency scattered by the diffuser. The width of the wells determine the highest frequency diffused. Manfred Schroeder's work on number theoretical acoustic diffusers gives us the following formulas:
            Lowest      ⁢                          ⁢      Diffused      ⁢                          ⁢      Frequency      ⁢                          ⁢              (        Hz        )              ≈                  Speed        ⁢                                  ⁢        of        ⁢                                  ⁢        Sound                    4        *                  (                      Depth            ⁢                                                  ⁢            of            ⁢                                                  ⁢            Deepest            ⁢                                                  ⁢            Well                    )                                Highest      ⁢                          ⁢      Diffused      ⁢                          ⁢      Frequency      ⁢                          ⁢              (        Hz        )              ≈                  Speed        ⁢                                  ⁢        of        ⁢                                  ⁢        Sound                    2        *                  (                      Width            ⁢                                                  ⁢            of            ⁢                                                  ⁢            Wells                    )                    
Schroeder explored the use of both quadratic residue and primitive root number sequences to determine the depth of wells in his diffusers.
FIG. A-1 shows an elevation of a Quadratic Residue sequence of depths based on prime number 7. Examples of other Quadratic-Residue Sequences with the prime number from which they are derived:
p=5: 0 1 4 4 1 0
p=7: 0 1 4 2 2 4 1 0
p=11: 0 1 4 9 5 3 3 5 9 4 1 0
p=13: 0 1 4 9 3 12 10 10 12 3 9 4 1 0
p=17: 0 1 4 9 16 8 2 15 13 13 15 2 8 16 9 4 1 0
p=19: 0 1 4 9 16 16 6 17 11 7 5 5 7 11 17 6 16 9 4 1 0
p=23: 0 1 4 9 16 2 13 3 18 12 8 6 6 8 12 18 3 13 2 16 9 4 1 0
Examples of Primitive-Root sequences and the prime number from which they are derived:
p=5: 2 4 3 1
p=7: 3 2 6 4 5 1
p=11: 2 4 8 5 10 9 7 3 6 1
p=13: 2 4 3 3 6 12 10 9 5 10 7 1
p=17: 3 9 10 13 5 15 11 16 14 8 7 4 12 2 6 1
p=19: 2 4 8 16 13 7 14 9 18 17 15 11 3 6 12 5 10 1 (Everest, 2001)
Commercially available as RPG Inc's Quadratic Residue Diffuser or QRD™
Peter D'Antonio et al Pat. No. D291601
Depicted in FIG. 2
Commercially named the QRD™ and called an Acoustic baffle in patent D291,601, this diffuser is essentially an embodiment of Manfred Schroeder's quadratic residue diffuser. A box is divided into a plurality of wells with thin dividers. The depth of these wells is varied based on quadratic residue number sequences. The wells are all rectilinear in shape, with the back of the wells parallel to the face of the diffuser. In the acoustic treatment industry, this design is probably the most copied of all of the other one-dimensional designs.
There are two disadvantages of this design:
First, this is a one-dimensional diffuser and thus diffusion only occurs laterally in a fan shaped pattern in a single dimension. In other words, sound is scattered to the sides but not up and down. If the QRD is installed so that the dividers run horizontally, then diffusion only occurs vertically.
Second, a rectilinear or box-shaped diffuser wastes valuable floor space. In order to diffuse lower frequencies, a QRD diffuser must be as deep front to back as possible. As mentioned in the discussion of Manfred Schroeder's research, the depth of the deepest well is ¼ the wavelength of the lowest affected frequency. For instance, a diffuser with a maximum well depth of 1 foot will diffuse frequencies up to 4 feet in length. Using the formula:
      λ    ⁡          (      Wavelength      )        ≈            Speed      ⁢                          ⁢      of      ⁢                          ⁢      Sound        Frequency  
We find that this lowest frequency is approximately 281.5 Hz.
A typical installation of a diffuser is on the rear wall of a critical listening space. A 1-foot-deep QRD diffuser would extend into the room a minimum of 1 foot trapping an unusable space below the diffuser where furniture or other items cannot be placed. At best, this space can be enclosed and used as cabinet storage or low shelving. Visually, the front of the dividers becomes the new location of the wall.
The Acoustic Ramp's wedge shape avoids both of the above mentioned disadvantages.
First, the Acoustic Ramp diffuses sound energy laterally much the same way that the QRD™ diffuses energy, and it also reflects the energy at several different angles vertically. For instance, in Embodiment 1 of the present invention, there are reflectors at approximately 0, 7, 10.5 and 14 degrees. The present invention is installed vertically with the deeper end in the upper corner made between the ceiling and wall. The Acoustic Ramp with scatter sound in all directions horizontally and reflect the sound down toward the floor and away from the sound source vertically.
Second, the variable depth of the wedge shape allows installation into upper corners, using this often unused space for diffusion. The diffuser tapers to flat as it descends the wall allowing furniture or other objects to be pushed all the way against the wall. This prevents the trapping of floor space exhibited by the QRD™ diffuser.
Burton E. Cullum et al U.S. Pat. No. 5,969,301
Depicted in FIG. 3
Burton Cullum's Acoustic Diffuser Panel System is essentially a two period quadratic residue diffuser based on the prime number 7 or the familiar 0 1 4 2 2 4 1 0 pattern. The biggest advantage of this invention is the possibility of molding the entire structure from a single piece of plastic. This will make the product significantly less expensive to manufacture. The disadvantages however are numerous.
The concave shape of the back of the wells serve to actually focus or amplify rather than diffuse the sound. The early pre-Schroeder attempts at diffusion were actually series of convex shapes in various permutations. The plastic used to mold a diffuser of this nature would need to be very rigid in order to reflect acoustic energy, but thin enough to make manufacturing cost effective.
Similarly to the QRD™ from RPG Inc, this diffuser will only diffuse energy laterally in a single dimension.
Jay Perdue U.S. Pat. No. 6,209,680
Depicted in FIG. 4
Perdue's Acoustic Diffuser Panels have some elements which on the surface might appear similar to the present invention. This diffuser has a modified-wedge shape, but the type of design diminishes the actual diffusive properties. The entire face of the diffuser panel is angled with respect to the back wall of the diffuser. Thus, the face will behave like a reflector, not as a diffuser. The tops and bottom of the wells are angled, but all of the angles in all of the wells are the same. Both of these features will offer very little improvement over 3 flat panels canted at 3 different angles. The wells offer no phase change to reflected sound because the wells are all the same distance away from the sound source. If the back of the diffuser was angled and not the front, this design would likely be significantly more effective.
The angled tops/bottoms of the wells will offer a little phase complexity, but the angle of all the tops/bottoms are the same, minimizing the effect. All of the lower sides of the wells will act as a single reflector, as will all of the upper sides of the wells. Purdue's diffuser could be better viewed as series of small reflectors with three different angles.
Commercially available as RPG Inc's Skyline™ two-dimensional diffuser
Peter D'Antonio et al U.S. Pat. No. 5,401,921
Depicted in FIG. 5
RPG Inc's Skyline™ diffuser is a 2-dimensional diffuser. This means that acoustic energy is diffused in two planes, both vertically and horizontally. It is likely that RPG Inc chose to use a primitive root number sequence because quadratic residue diffusers of the same style were no longer patentable after the BBC's 1990 paper on diffusers (Walker, 1990).
Both the upper and lower frequency limits are defined by the width and height of the square columns respectively. The length of the columns defines the lower frequency boundary, while the upper frequency boundary is defined by the width of the column.
One difficulty with this design lies in appropriate materials for manufacture. The columns must be rigid enough to reflect and not absorb acoustic energy. This means typical foam materials are not appropriate because they tend to absorb certain frequencies. Injection molding or vacuum molding are options, but the cost of the molds and dies to make the forms is quite high. RPG uses expanded polystyrene foam in their commercial models which offers a surface rigid enough to reflect frequencies up to the high frequency limit.
The DIY community commonly builds two dimensional quadratic residue diffusers, based on the BBC paper mentioned above, that are very similar to the Skyline™ diffuser from either wood or foam insulation. The foam insulation absorbs too much sound and the wood version is extremely heavy and hard to install onto walls as a result.
The Skyline diffuser shares the same problem with all of the others diffusers examined in that a deeper diffuser intrudes into the room too much and uses up valuable space. The Acoustic Ramp pushes the deepest part of the diffuser into the upper wall space which is typically unused. This allows diffusion to happen at lower frequencies without using up valuable floor space.
Commercially Available as Art Diffusors by Acoustics First
Bernard W. Chlop U.S. Pat. No. 5,160,816
Depicted in FIG. 6
Chlop's Two-Dimensional Diffuser is not as effective as RPG Inc's Two Dimensional Diffuser because the diffusion is not equal in both the horizontal and vertical plane. While this design also employs the use of square columns at different lengths protruding from a flat base, it does not use a randomizing number sequence to place the columns. Instead the design employs repeating patterns of columns of different heights. This repeated pattern will cause the diffuser to be much less two-dimensional than a near-random orientation of columns generated with a maximum length sequence of numbers.
One of the positive improvements of this design over prior art is the angled reflective ends of the square columns which likely reflects energy away from the sound source. Unfortunately, the rows of columns all have the same angle aligned in the same direction which minimizes this positive effect.